Let d > 1, and let (X,α) and (Y, β) be two zeroentropy Z-actions on compact abelian groups by d commuting automorphisms. We show that if all lower rank subactions of α and β have completely positive entropy, then any measurable equivariant map from X to Y is an affine map. In particular, two such actions are measurably conjugate if and only if they are algebraically conjugate.

In this thesis, I present an associative diagram algebra that is a faithful representation of a particular Temperley–Lieb algebra of type affine C, which has a basis indexed by the fully commutative elements of the Coxeter group of the same type. The Coxeter group of type affine C contains an infinite number of fully commutative elements, and so the corresponding Temperley–Lieb algebra is of in...

The articles [6], [1], [4], [5], [2], and [3] provide the notation and terminology for this paper. Let O1 be an ordered affine space. Then Λ(O1) is an affine space. Let O1 be an ordered affine plane. Then Λ(O1) is an affine plane. We now state several propositions: (1) There exists a real linear space V and there exist vectors u, v of V such that for all real numbers a, b such that a · u + b · ...

We generalize the results of hep-th/0701214 about the covariant c-map to include the perturbative quantum corrections. We also perform explicitly the superconformal quotient from the hyperkähler cone obtained by the quantum c-map to the quaternion-Kähler space, which is the moduli space of hypermultiplets. As a result, the perturbatively corrected metric on the moduli space is found in a simpli...

Let {Si}i∈Λ be a finite contracting affine iterated function system (IFS) on Rd. (Σ,σ) denote the two-sided full shift over alphabet Λ, and let π:Σ→Rd coding map associated with IFS. We prove that projection of an ergodic σ-invariant measure Σ under π is always exact dimensional, its Hausdorff dimension satisfies Ledrappier–Young-type formula. Furthermore, result extends to average IFSs. This c...

In this paper, we introduce a novel discrete chaotic map named zigzag map that demonstrates excellent chaotic behaviors and can be utilized in truly random number generators (TRNGs). We comprehensively investigate the map and explore its critical chaotic characteristics and parameters. We further present two circuit implementations for the zigzag map based on the switched current technique as w...

Let M be a connected oriented surface and let G'2 be the Grassmannian of oriented 2-planes in Euclidean (2 + c)-space. E2 + l. Smooth maps t: M -» (7f are studied to determine whether or not they are Gauss maps. Both local and global results are obtained. If í is a Gauss map of an immersion X: M -» E2 + 1, we study the extent to which / uniquely determines X under certain circumstances. Let X: ...

where we view Gm(S) as the subgroup of invertible scalars in GLn(S). Define PGLn = s ◦ P̃GLn to be its sheafification (taken in the sense of Problem 8 on PS 2). Our goal will be to show that PGLn is an affine group scheme that represents automorphisms of projective space in the sense that PGLn(S) ' AutS(S × Pn−1). Before we begin, we require some preliminaries about Zariski sheaves. Let F : Sch→...

A new method is presented for identifying and comparing closed, bounded, free-form curves that are defined by even implicit polynomial (IP) equations in the Cartesian coordinates x and y. The method provides a new expression for an IP involving a product of conic factors with unique conic factor centers. The critical points for an IP curve also are defined. The conic factor centers and the crit...

This paper is devoted to studying boundedness criteria for extended-real-valued functions. The study is done in the framework of dual vector spaces, using new objects such as self-equilibrated sets and functions. We establish two boundedness new major criteria. The first one says that an extended-real-valued function is bounded below provided it is minorized by an affine map on one of its self-...